Finite Group Databasebeta

← #20250283

Subgroups — #20250283

Order 6016.

434 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094018C211yesmaximal, characteristic
2C2×#13094014C211yesmaximal, characteristic, complemented
3#15689058C211yesmaximal, characteristic
4#15689058C211yesmaximal, characteristic
5#15689057C211yesmaximal, characteristic, complemented
6#15689056C211yesmaximal, characteristic, complemented
7#15689052C211yesmaximal, characteristic
8#15689045C211yesmaximal, characteristic
9#15689015C211yesmaximal, characteristic
10#15689013C211yesmaximal, characteristic
11#15689007C211yesmaximal, characteristic, complemented
12#15689005C211yesmaximal, characteristic, complemented
13#15689004C211yesmaximal, characteristic, complemented
14#15688992C211yesmaximal, characteristic, complemented
15C47×#389C211yesmaximal, characteristic, complemented
16#13094018—24no—
17#13094014—24no—
18C2×C4⋊Dic47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×C4×Dic47C2211yescharacteristic
37C2×C4×Dic47C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50C2×C42×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C23×D47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C4⋊C4×C47—22no—
69C4⋊C4×C47—22no—
70C4⋊C4×C47—41no—
71C4⋊C4×C47—41no—
72C42×C47—22no—
73(C2×D47)⋊C4—22no—
74(C2×D47)⋊C4—22no—
75(C2×D47)⋊C4—22no—
76(C2×D47)⋊C4—22no—
77(C2×D47)⋊C4—22no—
78(C2×D47)⋊C4—41no—
79(C2×D47)⋊C4—41no—
80C4⋊Dic47—22no—
81C4⋊Dic47—41no—
82Dic47⋊C4—22no—
83Dic47⋊C4—22no—
84Dic47⋊C4—22no—
85Dic47⋊C4—22no—
86Dic47⋊C4—22no—
87Dic47⋊C4—22no—
88Dic47⋊C4—22no—
89Dic47⋊C4—41no—
90Dic47⋊C4D414yes—
91C4×Dic47—22no—
92C4×Dic47—22no—
93C23×C47C2411yescharacteristic
94C22×D47—21no—
95C22×D47—21no—
96C22×D47—21no—
97C22×D47—21no—
98C22×D47—21no—
99C22×D47—21no—
100C22×D47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47C2×D412yes—
121C2×C4×C47#4112yes—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47C2×D412yes—
141C2×Dic47C2×D412yes—
142C2×Dic47#4112yes—
143C22×C47C22×D411yescharacteristic
144C22×C47C2×#4111yescharacteristic
145C22×C47C2×#4111yescharacteristic
146C22×C47H(5,𝔽2)11yescharacteristic
147C22×C472−1+411yescharacteristic
148C22×C472−1+411yescharacteristic
149C22×C472−1+411yescharacteristic
150C2×D47—41no—
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C4×C47—22no—
158C4×C47—22no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47—41no—
164Dic47—22no—
165Dic47—22no—
166Dic47—22no—
167Dic47—41no—
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171#2721—471nomaximal, Sylow
172C2×C47#53611yescharacteristic
173C2×C47#53911yescharacteristic
174C2×C47#54111yescharacteristic
175C2×C47#54711yescharacteristic
176C2×C47#55011yescharacteristic
177C2×C47#55211yescharacteristic
178C2×C47#56311yescharacteristic
179D47—81no—
180C2×#126—471no—
181C2×#125—471no—
182#399—471no—
183#399—471no—
184#398—471no—
185#398—471no—
186#397—471no—
187#396—471no—
188#389D4711yescharacteristic, complemented
189#388—471no—
190#388—471no—
191#387—471no—
192#387—471no—
193#387—471no—
194#384—471no—
195C47#272111yescharacteristic, complemented, Sylow
196#126—944no—
197#125—944no—
198C2×C4⋊C4—471no—
199C2×C4⋊C4—471no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4—471no—
206C2×C4⋊C4—471no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4C2×D4711yescharacteristic
210C2×C4⋊C4C2×D4711yescharacteristic
211C2×C4⋊C4C2×D4711yescharacteristic
212C2×C4⋊C4C2×D4711yescharacteristic
213C2×C22⋊C4—471no—
214C2×C22⋊C4—471no—
215C2×C22⋊C4—471no—
216C2×C22⋊C4—471no—
217C2×C22⋊C4—471no—
218C2×C22⋊C4—471no—
219C2×C22⋊C4—471no—
220C2×C42—471no—
221C2×C42—471no—
222C2×C42C2×D4711yescharacteristic
223#95—471no—
224#95—471no—
225#95—471no—
226#95—471no—
227#95—471no—
228#95—471no—
229#95—471no—
230#95—471no—
231#95C2×D4711yescharacteristic
232#95C2×D4711yescharacteristic
233C24—471no—
234C22×C4—471no—
235C22×C4—471no—
236C22×C4—471no—
237C22×C4—471no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4C22×D4711yescharacteristic
242C22×C4C22×D4711yescharacteristic
243C22×C4C22×D4711yescharacteristic
244C22×C4C22×D4711yescharacteristic
245C22×C4C22×D4711yescharacteristic
246C22×C4C22×D4711yescharacteristic
247C22×C4C22×D4711yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—474no—
253C4⋊C4—942no—
254C4⋊C4—942no—
255C4⋊C4—942no—
256C4⋊C4—942no—
257C4⋊C4—942no—
258C4⋊C4—942no—
259C4⋊C4—942no—
260C4⋊C4—942no—
261C4⋊C4—1881no—
262C4⋊C4—1881no—
263C22⋊C4—942no—
264C22⋊C4—942no—
265C22⋊C4—942no—
266C22⋊C4—942no—
267C22⋊C4—942no—
268C22⋊C4—1881no—
269C22⋊C4—1881no—
270C42—22no—
271C42—942no—
272C42—942no—
273C23—941no—
274C23—941no—
275C23—941no—
276C23—941no—
277C23—941no—
278C23—941no—
279C23—941no—
280C23C23×D4711yescharacteristic
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—472no—
301C2×C4—472no—
302C2×C4—472no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4#1062535012yes—
322C2×C4D4×D4712yes—
323C22—1881no—
324C22—1881no—
325C22—1881no—
326C22—1881no—
327C22—1881no—
328C22—1881no—
329C22—1881no—
330C22C2×D4×D4711yescharacteristic
331C22#41×D4711yescharacteristic
332C22C2×#1062535011yescharacteristic
333C22#1309406911yescharacteristic
334C22#1309407111yescharacteristic
335C22#1309407211yescharacteristic
336C22#1309407211yescharacteristic
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—942no—
345C4—942no—
346C4—942no—
347C4—1881no—
348C4—1881no—
349C4—1881no—
350C4—1881no—
351C2—3761no—
352C2#1568969611yescharacteristic
353C2#1568971511yescharacteristic
354C2#1568973211yescharacteristic
355C2#1568977411yescharacteristic
356C2#1568979111yescharacteristic
357C2#1568981411yescharacteristic
358C2#1568987211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#389C2
hypercenter#389D47
hypocenterC47#2721
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #389

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#13094014C2semidirect
5. #15689057C2semidirect
6. #15689056C2semidirect
11. #15689007C2semidirect
12. #15689005C2semidirect
13. #15689004C2semidirect
14. #15688992C2semidirect
15. C47×#389C2semidirect
188. #389D47semidirect
195. C47#2721semidirect